Satellite locations may have to be estimated in the scope of a satellite signal based positioning.
A satellite signal based positioning may be based for example on any kind of present and/or future Global Navigation Satellite System (GNSS), such as the Global Positioning System (GPS), GLONASS, Galileo, the BeiDou Navigation Satellite System (BDS), etc., or any combination thereof.
In a GNSS system, satellites orbiting the Earth transmit signals that a receiver may use to calculate its own position. The signals transmitted by a satellite convey a message, and a part of the message comprises a set of parameter values of an orbit model defining an orbit of the satellite for a limited period of time. Such parameter values are referred to in some of the GNSSs as the broadcast ephemeris (BE). They can be used by the receiver to compute the location of the satellite, for example in an Earth-Centered-Earth-Fixed (ECEF) coordinate system. Based on the estimated locations of a plurality of satellites and the propagation time of the signals, the receiver may compute its own position. The propagation time may be estimated from a time of transmission of the satellite signal indicated in the message and a measured time of arrival of the satellite signal at the receiver. The parameter values of the orbit model have a certain, limited validity time, during which the satellite's location can be estimated with a desired accuracy. Positioning accuracy decreases as the age of the parameter values for a satellite increases, and eventually the receiver must receive a new set of parameter values of the orbit model before it can continue with positioning.
It is possible to extend the usability of a received broadcast ephemeris beyond its intended lifespan. A corresponding method may be referred to as Ephemeris extension service (EES). It is usually performed on-device at the receiver, with or without the usage of external assistance data.
In a typical EES system, the orbit of a satellite is predicted by integrating output values of an equation of motion defined for the satellite. The last reliable satellite location that can be determined with broadcast ephemeris data may be used as an initial state of the orbit for the integration. The equation of motion is also called force model, as it is based on forces acting on the satellite. Ideally the equation of motion includes all the forces affecting the satellite. However, in practice it may not feasible to model all the forces and typically the equation of motion includes only the four major forces: gravitational forces of the Earth, the Sun and the Moon and solar radiation pressure.